A numerical method to account for distance in a farmer's willingness to pay for land

Land transactions between farmers are responsible for landscape changes in rural areas. The price a farmer is willing to pay (WTP) for vacant land depends on the distance of the parcel to the farmstead. Detailed quantitative knowledge of this WTP- distance relationship is of utmost importance for accurate modelling of land markets, and for the design and implementation of effective and robust land consolidation schemes. Practical experience suggests, however that it is not particularly easy to back out the WTP-distance relationship from empirical transaction data. Here, we present a novel statistical framework to help quantify the relationship between a farmer's WTP and the distance of his/her farmstead to the vacant parcel. We describe a land market with a simple statistical model and simulate an artificial archive of land transactions via Monte Carlo sampling. The parameters of our virtual market are estimated from a historical archive of land transactions in the Province of Gelderland The Netherlands, using minimization of the divergence (relative entropy) between the observed and simulated joint distributions of distance and transaction price. A reasonable agreement was observed between the observed and simulated bivariate distributions of distance and transaction price. Our results demonstrate that for short distances (500-1000m) any additional metre distance reduces the WTP by about 60 € ha-1. The impact of distance on WTP gradually levels off with larger distance: beyond 5 km the effect has reduced to less than 0.5 € ha-1